Problem: The following line passes through point $(-6, -3)$ : $y = \dfrac{9}{11} x + b$ What is the value of the $y$ -intercept $b$ ?
Answer: Substituting $(-6, -3)$ into the equation gives: $-3 = \dfrac{9}{11} \cdot -6 + b$ $-3 = -\dfrac{54}{11} + b$ $b = -3 + \dfrac{54}{11}$ $b = \dfrac{21}{11}$ Plugging in $\dfrac{21}{11}$ for $b$, we get $y = \dfrac{9}{11} x + \dfrac{21}{11}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-6, -3)$